The "Fluctuation Model" for the generation of ultrashort pulses by a saturable absorber has been discussed by a number of authors. This model has provided valuable insights into the mechanisms involved in passive mode locking; however, previous treatments have been incorrect in several important respects. These treatments have attempted to describe the behavior of the laser in terms of the evolution of a statistically independent set of fluctuations (pulses) circulating in the laser. It is shown here that such a description is impossible in principle. This paper discusses in detail the problem with the previous treatments and presents an alternate treatment of the evolution of the ultrashort pulses during the nonlinear phase of development. The model is capable of predicting the conditions under which good mode locking will occur, the probability of the appearance of secondary pulses and their relative intensities, the peak intensity of the output pulse train and its statistical variation, and the duration and time of appearance of the output pulse train. The analysis has also been formulated in such a way that the evolution of the signal can be followed by measurement of experimentally observable quantities.